Question

Use the Angle Addition Postulate and the given information to complete each statement. If H is in the interior of ∠EFG, m∠EFH = 65°, m∠HFG = (5x)", and m∠EFG = (20x+5)', what is the m∠HFG? *

Answer 1

To find the measure of angle HFG, use the Angle Addition Postulate. Set up and solve an equation to find the value of x. Substitute the value of x back into the equation to find the measure of angle HFG, which is 20°.

Step-by-step explanation:

To find the measure of angle HFG, we can use the Angle Addition Postulate. According to the postulate, the sum of the measures of two adjacent angles is equal to the measure of the larger angle. In this case, we have angle EFH with a measure of 65° and angle HFG with a measure of 5x. We also have angle EFG with a measure of 20x+5°.

Using the Angle Addition Postulate, we can set up the equation: 65 + 5x = 20x + 5.

Simplifying the equation, we get 60 = 15x.

Dividing both sides by 15, we find that x = 4.

Substituting x = 4 back into the equation for m∠HFG, we get m∠HFG = 5x = 5(4) = 20°.